The lack of simplicity in sequence-fitness relationships

Gene interactions play an important role in the development of antimicrobial drug resistance and other evolutionary processes of medical importance. Empirical studies have revealed multiple peaks, inaccessible trajectories, and constraints on mutation order. Higher order epistasis is associated with obstacles in fitness landscapes. However, its significance has been debated in recent years, sometimes through reinterpretations of data from previous publications.

We suggest that local higher order interactions may help reconcile these seemingly contradictory findings. Rank order based methods can be informative when other methods fail to detect consequential interactions. In addition to conventional rank order methods, including sign epistasis, we introduce signed bipyramids. A bipyramid interaction compares extreme genotypes against their intermediates, for example a triple mutant and the wild-type against the corresponding single mutants. In general, interactions are signed if they are implied by the rank order alone.